This will be an Illinois case as the children reside in Illinois. The children are in the father's custody, so I don't think you have standing to seek custody under the Marriage and Divorce Act. You also have a very low probability of success under the guardianship statute. You would need to show the parent voluntarily relinquished custody and is unwilling or unable to care for the children or have him consent to the guardianship.
If he is neglecting or abusing the children, it may be possible to get DCFS involved, but only recommend this in extreme cases -- you never know what exactly a governmental agency will do. They could send the children to a different family member or an unrelated caretaker and the risk of this, even if unlikely, may not be worth it. Definitely consult an attorney and think long and hard before going down this path. There are a lot of possible unintended consequences.
You may have standing, however, to seek visitation with the children. Again, the burden of proof would be on you in such a proceeding.
This is a case that will need special handing. You need to convince him to perhaps take the kids for the summer. Then you may be able to get standing to go to court. It has to be handled very carefully so as not to get DCFS involved if at all possible. Contact a family law attorney and start making a plan. You will need to contact an Illinois attorney first. You can call the police in his town and have them check on the children. this is common.
IF YOU FOUND THIS ANSWER "Helpful" or " The Best Answer" YOU CAN THANK ATTORNEY RADDATZ BY MARKING IT SO because Avvo awards the attorney points. MS. RADDATZ is donating her time and talent by answering questions to help those in need of legal information. This is NOT a consultation and in no way creates an attorney-client relationship. YOU SHOULD ALWAYS PERSONALLY CONSULT WITH AN ATTORNEY IN YOUR LOCAL AREA who has specific expertise in the area of law you are asking about.